W.F. Langford, R. Tagg, E. Kostelich, H.L. Swinney and M. Golubitsky
Primary instability and bicriticality in flow between counterrotating cylinders
Phys. Fluids. 31 (4) (1988) 776-785.
The primary instabilities and bicritical curves for flow between counter-rotating cylinders have been computed numerically from the Navier-Stokes equations assuming axial periodicity. The computations provide values of the Reynolds numbers, wavenumbers, and wave speeds at the primary transition from Couette flow for radius ratios from 0.40-0.98. Particular attention has been focused on the bicritical curves that separate (as the magnitude of counter-rotation is increased) the transitions from Couette flow to flows with different azimuthal wavenumbers m and m + 1. This lays the foundation for further analysis of nonlinear mode interactions and pattern formation occuring along the bicritical curves and serves as a benchmark for experimental studies. Preliminary experimental measurements of transition Reynolds numbers and wave speeds presented here agree well with the computations from the mathematical model.